Sen. Ted Cruz of Texas announced Monday that he is running for president, making him the first official candidate in the 2016 race for the White House.

“I believe God isn’t done with America yet,” Mr. Cruz said during a speech at Liberty University, sending a strong signal that he plans to compete for the evangelical Christians that traditionally play a big role in the GOP nomination race.

“I believe in you. I believe in the power of millions of courageous conservatives rising up to reignite the promise in America,” he said. “And that is why today I am announcing that I am running for president of the United States.”

The big question for Mr. Cruz is whether he can build a big enough coalition to claim the mantle of the conservative alternative to the establishment candidate in a Republican race that will likely also feature former Florida Gov. Jeb Bush, Wisconsin Gov. Scott Walker and Sen. Rand Paul of Kentucky.

Mr. Cruz is running near the middle of the pack in early national polls, behind Mr. Bush, Mr. Walker and Mr. Paul, who is planning to enter the race early next month.

Ford O’Connell, a GOP strategist, said Mr. Cruz has a “narrow” path to the nomination.

“For Cruz to have a legitimate shot at the nomination, he has to become the preeminent candidate for both grassroots conservatives and social conservatives, which means he has to elbow out the darlings of social conservatives — Mike Huckabee, Rick Santorum and Ben Carson,” Mr. O’Connell said.